Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 Algorithm for describing the Terwilliger and quantum adjacency algebras of a distance-regular graph 975 984 14874 10.22049/cco.2024.29114.1874 EN Abdillah Ahmad Master Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia John Vincent Morales Department of Mathematics and Statistics, De La Salle University, Manila, Philippines Pritta Etriana Putri Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia Journal Article 2023 11 10 In this paper we consider an algorithm for determining a basis for the Terwilliger and quantum adjacency algebras of a distance-regular graph. For the Terwilliger algebra, we consider the generating set. For the quantum adjacency algebra, we consider the generating set consisting of the raising, flat, and lowering matrices. We give optimization method by using generating matrices with a block-matrix structure so that the number of matrix multiplications required is reduced. https://comb-opt.azaruniv.ac.ir/article_14874_806405ed152175692394b8ae0ff3594e.pdf